I am reading the paper named " Array performances for ambient vibrations on a shallow structure and consequences over Vs inversion (Marc Wathelet, et. al)". I got one question. In the Figure 5 and 6, you have shown that the calculated dispersion curves will deviate from the theorectical ones at frequencies below some frequency (close to the fundamental resonance frequency). As far as I observed, why do they all deviate to higher velocities? This makes it look like that they jump to the higher modes. Thanks very much.

Close to and below the resonance frequency the energy available on the vertical component for Rayleigh wave drops down, hence poor results in terms of velocity estimates can be achieve at that frequency. Among other things, this drop produces the peak of the H/V curve if Rayleigh waves dominate in the vertical component of the noise.

The deviation towards higher velocities that you can observe in figures 6a to 6b (to a lesser extent 5b) is mainly linked to the geometry of the arrays. If you look carefully to figure 6a and 6b, you can see that the deviation occurs at a higher frequency than the resonance (3-4 Hz while resonance is at 2Hz). The results plotted in figures 6a and 6b are related to arrays with a smaller aperture compared to figure 6c or 5b. The aperture of the array directly controls the resolution power of the technique (in this case, the resolution is the ability to distinguish two waves traveling at the same time with slightly different wave numbers). Small arrays are not able to identify correctly small wave numbers (high velocity), leading to an over estimation of the real velocity.

Arrays of figures 6c and 5b are designed so that they cover the whole frequency range down to and below the resonance frequency: but no matter the size of the array, the kick-off corresponds to the resonance frequency. In this case, we probably observe a mixture of lack of resolution due to array size and of lack of energy on the vertical component. Interestingly array D (figure 6c) is far bigger than array C (figure 5b) and no better results can be achieved. In this sense, the resonance frequency appear to be a lower limit for the correct measurement of the dispersion curve from vertical component in a shallow structure. For real sites, far below this shallow resonance frequency (e.g. around 0.5 Hz), sufficient energy may be encountered but related to bigger geological structures.

Finally, I don't think that higher modes can be suspected at that frequency.